Phase-contrast magnetic resonance imaging (PC-MRI) is a noninvasive technique capable of quantifying hemodynamics in the heart and great vessels. Because spin moving through a spatially varying magnetic field accumulates phase compared to static spin, velocity information in PC-MRI is encoded into the phase of the complex-valued image. This information is then retrieved by measuring the phase differences between images collected under different values of the velocity-encoding gradients. Cardiovascular applications of PC-MRI include quantification of cardiac function, evaluation of stenosis, assessment of congenital heart disease, and evaluation of aortic atherosclerosis.
Clinical application of PC-MRI to 4D flow imaging and to real-time through-plane velocity imaging has been precluded by long scan times and low acquisition efficiency. Several methodological improvements have been proposed to reduce acquisition time of flow imaging via PC-MRI: parallel MRI (pMRI), fast sampling strategies, and iterative image recovery inspired by compressive sensing (CS) concepts. For 2D PC-MRI, Kim et al. proposed k-t SPARSE-SENSE and reported a six-fold acceleration for liver imaging with electrocardiogram triggering; k-t SPARSE-SENSE combines randomized Cartesian sampling, pMRI, and sparsity of temporal principal components analysis (PCA). More recently, Giese et al. individually processed principal components from multiple spatial compartments in the image series to capture the spatially varying dynamic behavior. Kwak et al. recovered five-fold accelerated 2D PC-MRI by enforcing total variation (TV) minimization of both encoded and compensated images as well as exploiting the sparsity of the complex difference image. Most 2D PC-MRI reconstruction methods can be extended for 4D flow where even higher acceleration is possible due to additional redundancy. Knobloch et al. proposed a method that utilizes both temporal PCA and the complex difference of velocity-encoded and velocity-compensated images to report an eight-fold acceleration for 4D flow. Despite these proposed processing methods, the challenge remains to achieve 4D flow imaging in clinically relevant acquisition times.